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Nonthermal Hard X-Ray Radiation from Solar Flares: Observations and Models

Nonthermal Hard X-Ray Radiation from Solar Flares: Observations and Models. Gordon D. Holman Laboratory for Solar and Space Physics NASA Goddard Space Flight Center. What do we mean by “hard X-rays and “nonthermal radiation”?. Hard X-rays : 10 keV – 300 keV, between soft X-rays and gamma-rays

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Nonthermal Hard X-Ray Radiation from Solar Flares: Observations and Models

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  1. Nonthermal Hard X-Ray Radiation from Solar Flares: Observations and Models Gordon D. Holman Laboratory for Solar and Space Physics NASA Goddard Space Flight Center

  2. What do we mean by “hard X-rays and “nonthermal radiation”? • Hard X-rays: 10 keV – 300 keV, between soft X-rays and gamma-rays • Nonthermal radiation: radiation from an electron distribution that is not locally Maxwellian

  3. First X-ray Observations • X-rays first observed from the Sun by Friedman (Naval Research Lab.) with Geiger counters on a V-2 rocket in 1949 • First detection of a solar flare in hardX-rays/-rays: 1958 by Peterson & Winckler (Univ. of Minnesota) during a balloon flight from Cuba (1958 Physical Review Letters)

  4. First Image of Hard X-ray Footpoints? Solar Maximum Mission (SMM)Hard X-ray Imaging Spectrometer (HXIS) Hoyng et al., The Astrophysical Journal Letters, 1981

  5. Spectra from the Solar Maximum Mission Hard X-Ray Burst Spectrometer Dennis, Solar Physics, 1985

  6. Flare Spectra Obtained with Cooled Germanium Detectors - 1980 Balloon Flight 34 MK “superhot” plasma Lin et al., The Astrophysical Journal Letters, 1981 Double power-law spectra Lin & Schwartz, The Astrophysical Journal, 1987

  7. SMM HXRBS Spectra Indicating a Thermal Component at Low Energies 3 February 1982 Kiplinger et al., The Astrophysical Journal, 1989

  8. electron photon From Fast Electrons to Bremsstrahlung Photons Nv electrons cm-2 s-1 nions cm-3 Bremsstrahlung Cross section (cm2) Nph = nNv photons s-1 cm-3 Nv photons s-1 ion-1

  9. From an Electron Distribution Function to a Bremsstrahlung Spectrum Nph(ε, E) = nN(E)v(ε, E) ε = photon energy E = electron energy Differential cross section(ε, E) = d(ε, E)/dε Electron Flux Distribution Function F(E) = N(E)v electrons cm-2 s-1 keV-1 Nph(ε) = n εF(E)(ε, E) dE photons s-1 cm-3 keV-1

  10. Photon Flux at Detector& Mean Electron Flux I(ε) = (1/4R2) Vn(r)εF(E,r)(ε, E) dE dV photons s-1 cm-2 keV-1 R = 1 AU I(ε) = (1/4R2) ε[Vn(r)F(E,r) dV](ε, E) dE I(ε) = (1/4R2) nV εF(E)(ε, E) dE photons s-1 cm-2 keV-1 Mean Electron Flux:F(E) = (1/nV) Vn(r)F(E,r) dV

  11. Thick-Target Bremsstrahlung I I(ε) = (1/4R2) V ε n(r) F(E,r) (ε, E) dE dV I(ε) = (1/4R2) xεn(x) F(E,x) (ε, E) dE dx For a steady state and E = E(x), electron flux conservation gives F(E,x) dE = F(E0) dE0 F(E,x) (dE/dx) dx= F(E0) dE0 F(E,x) dx = F(E0) dE0 / (dE/dx) I(ε) = (1/4R2)   εF(E0) E0 [ n(x) (ε, E) / (dE/dx) ] dE dE0

  12. Thick-Target Bremsstrahlung II I(ε) = (1/4R2) εF(E0) E0ε[ n(x) (ε, E) / (dE/dx) ] dE dE0 For collisional energy losses in a fully ionized plasma, dE/dx =  K n / E I(ε) = (1/K4R2) εF(E0) [ εE0(ε, E) E dE ] dE0 Independent of plasma density, n(x)! Can deduce the injected electron flux distribution,F(E0) electrons s-1 keV-1

  13. Accelerated ElectronNumber Flux & Energy Flux dNel/dt =  F(E0) dE0 electrons s-1 dWel/dt =  E F(E0) dE0 erg s-1

  14. The Bremsstrahlung Cross Section • Nonrelativistic approximations • Kramers:(ε, E) = 0 /εE • Bethe-Heitler:(ε, E) = (0 /εE) ln[ (E/ε)1/2 + (E/ε - 1)1/2 ] • For relativistic, angle dependent, and polarization dependent cross sections, see Koch & Motz, Reviews of Modern Physics, 1959, and Haug, Astronomy & Astro-physics, 1997.

  15. Approximate Results for Power-Law Electron Distributions(Brown, Solar Physics, 1971) • Assume I(E)  E (photons s-1 cm-2 keV-1) • Thin target: F(E)  E (  1) (electrons cm-2 s-1 keV-1) • Thin target: N(E)  E(  ½) (electrons cm-3 keV-1) • Thick target:F(E0) E0(+1) (electrons s-1 keV-1)

  16. Spectra from Electron Distributions with a Low-Energy Cutoff N(E) = KE-5el. cm-3 keV-1 N(E) = KE-3el. cm-3 keV-1 Holman, The Astrophysical Journal, 2003

  17. Spectra from Electron Distributions with a High-Energy Cutoff N(E) = KE-3el. cm-3 keV-1 N(E) = KE-5el. cm-3 keV-1 Holman, The Astrophysical Journal, 2003

  18. Forward Fit to a RHESSI Flare Spectrum 23 July 200200:30:00 – 00:30:20 UT ( Observed Flux – Model Flux ) /  Best-Fit Model Mean Electron Flux Electron Distribution Holman et al., The Astrophysical Journal Letters, 2003

  19. Spectral Fits to the 15 April 2002 Flare Sui et al., ApJ, 2005

  20. Regularized Inversion of the July 23 Spectrum Compared with the Forward Fit Result Piana et al., The Astrophysical Journal Letters, 2003

  21. Photon Spectra from Theoretical Electron Distributions with “Interesting Features” Brown et al., The Astrophysical Journal, 2006

  22. Three Inversions and a Forward Fit to the Theoretical Photon Spectra

  23. Alternative Emission Mechanisms • Inverse Compton Radiation • Synchrotron Radiation • Inverse (proton-electron) bremsstrahlung • Electron-electron bremsstrahlung – becomes significant at energies above ~100 keV

  24. Anisotropic Electron Distribution  0 photon Massone et al., The Astrophysical Journal, 2004

  25. Compton Backscattered Photons (Albedo) Kasparova et al., Solar Physics, 2005

  26. Partially Ionized Thick Target Brown, Solar Physics, 1973

  27. Time Delays & Electron Propagation Aschwanden et al., The Astrophysical Journal, 1995

  28. Hard X-Ray PolarimetryX4.8 Flare of 23-July-2002 20 - 40 keV Polarization Mark McConnell, UNH

  29. Model Flare Loop with Cusp

  30. Model Loop in Hard X-Rays

  31. Change with Plasma Density in Loop

  32. Computed Spectra

  33. Energy Deposition

  34. Presentations at the SPD Meeting • Oral • 27.05, Wednesday June 28, 10:50 AM – 12:25 PM: Wei Lu X-ray Emission from Flaring Loops: Comparison Between RHESSI Observations and Hydrodynamic Simulations • 28.05, Wednesday June 28, 1:30 – 3:00 PM: Linhui Sui Motion of 3-6 keV Nonthermal Sources Along a Flare Loop • Poster • 13.15: Gordon Holman Understanding X-Ray Source Motions in a Solar Flare Loop

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